JP6404909B2 - How to calculate the output model of a technical system - Google Patents

Description

  The present invention relates to a method for calculating a model for an output quantity of a technical system that is nonlinearly dependent on a plurality of input quantities in an input quantity vector format, and has a plurality of model parameters as a model. One model structure is set, and these model parameters are optimized by an iterative method based on the measured output from the test bench experiment in the technical system, and multiple test bench experiments are performed according to the experiment plan. A plan is created from the estimated output of the model for each iteration step.

  The output of many technical systems is multidimensional, non-linear and depends on multiple parameters. A typical example is an internal combustion engine. In this case, for example, many characteristic values (output amounts) such as NOx emission, soot in exhaust gas, fuel consumption, and the like are applied to the rotational speed, torque, temperature, throttle valve Depends on various input quantities (or operating points) such as state, fuel pressure, etc. In general, a technical system (system) means that a predetermined number of specific input quantities such as a plurality of set values of a plurality of actuators, for example, a predetermined number of specific output quantities such as a characteristic value or a quantity measurable by a sensor. This means a system in which some kind of functional relationship exists between the input quantity and the output quantity. When developing such a technical system, it is quite expensive to develop exclusively on the test bench. This is because optimizing many non-linear output quantities that depend on various input quantities and also interdependencies is difficult to do manually. This is one development goal that can be envisaged. For this reason, it has already been attempted to imitate such a technical system, that is, a specific output quantity depending on the input quantity and the system parameters by using some mathematical models. Based on these models, the effects of fluctuations in input quantities and model parameters can be simulated and examined in detail, and some optimizations can be attempted, and then, for example, on a test bench Optimization is verified. In this regard, a so-called model-based method (model-based design of experiments) is known from, for example, US Pat. To identify a model of the technical system. In that case, for example, a model structure such as a known local model network (LMN) or a known multilayer perceptron (MLP) is selected, and model parameters are estimated based on data obtained from a test bench experiment (online). . At this time, the model repeatedly generates an output amount, and this output amount is used in the experimental design to generate a new input amount for the next iteration step. Began use on test benches for technical systems. The output of the test bench experiment is then used to improve the model parameters taking into account specific boundary conditions. This is repeated until the set stopping condition is satisfied, that is, until the model parameters are estimated sufficiently accurately. In doing so, what is important for estimating the model parameters is that the experimental design covers all dynamic ranges (Dynamics) and all output ranges of the technical system in order to obtain sufficient model quality in all output ranges. That is.

  However, many characteristic values of technical systems are important only in a certain range. The reason is that there is a law and the law sets a standard for a characteristic value in a specific variable area, or that a certain characteristic value is persuasive only in a specific variable area. Whatever the reason, why. Typical examples are NOx emissions and soot emissions of internal combustion engines, which must comply with limits set by legislative engines in specific operating ranges of internal combustion engines. Therefore, the model of such a characteristic value will have to be accurate only within the above-mentioned target output range (target output range) (Zielousgangsberich), but not to all possible output ranges. That is not necessary.

  However, the method of identifying a model based on a model (on a model basis) according to Patent Document 1 is effective for the entire output range, although the model is constructed. High cost, which has also led to the cost for the necessary test bench experiments in particular. On the other hand, because too little training data was used in the target output range to identify the model, the model might produce results that are not accurate enough in the target output range, of course. obtain. Therefore, such a model can be used only under limited conditions for the target output range.

  Non-Patent Document 1 reveals a method of creating an experiment plan so that the output amount is estimated as accurately as possible in the vicinity of a target range where the metamodel is narrow. A Kriging model is used as the meta model, and the target range is defined as a contour line. Therefore, although the model can be estimated very accurately in the vicinity of the contour line, it does not do so when it is within a larger target output range where this method is not suitable. In this method, a sequential experiment design method is applied, and a new input quantity is selected according to an optimization criterion that depends on both the known input quantity and the output quantity calculated correspondingly. Therefore, this method can be done without a test bench experiment. Therefore, the purpose of this method is not to perform optimization based on accurate measurements from test bench experiments in an actual system (actual system), but rather to fit a function to the set contours. There is.

International Publication No. 2012/163 972

Picheny, V.M. , Et al. ,? Adaptive Designs of Experiments for Accurate Application of a Target Region ", Journal of Mechanical Design, Vol. Hametner, C.I. , Et al. ,? Local model network identification for online engine modeling ", 2013, Information Sciences 220 (0), S.210-225.

  An object of the present invention is a method for calculating a model related to the output amount of a technical system, in which a test bench experiment is used for optimization, and the cost for the test bench experiment can be minimized as much as possible. The object is to provide a method in which the estimation model has high accuracy in a large target output range.

  This task calculates a set of output quantities from a set of input quantity vectors using a valid model that is effective for the current iteration step, and sets the target output from the set of output quantities. A target input quantity vector that yields an output quantity within the competence range is identified, and from the identified target input quantity vector, a new input quantity vector is selected for the next iteration step, and the above input quantity vector is selected. At this time, this new input quantity vector is selected according to a predetermined selection criterion based on the distance, and the set by the selected input quantity vector thus expanded is experimentally designed. As a result, the measurement data of the output amount is generated by the test bench experiment, the model is optimized using these measurement data, and the set stop condition is satisfied. It is solved by repeating the above method steps iteratively. In this way, the model is targeted and trained in a defined target output range, so fewer test bench experiments are achieved, yet nevertheless achieving very high accuracy within the target output range. be able to.

  The selection criterion based on distance takes into account the reference in the input amount range, the reference in the output amount range, or the reference in the input / output amount range.

  It has proved particularly preferable to use a local model network as the model structure. This is because this method requires only a small calculation cost, can utilize existing knowledge about technical systems, and derives model parameters that can be used for experiment planning in a robust manner.

  In the following, the present invention will be described in detail on the basis of FIGS. 1 to 10, which show schematically advantageous embodiments of the invention by way of example and without limitation. The figure shows:

Fig. 2 is a schematic diagram of the flow of the method according to the invention. FIG. 4 shows different iteration steps for a distance-based selection criterion in the input / output quantity range of the method according to the invention. FIG. 4 shows different iteration steps for a distance-based selection criterion in the input / output quantity range of the method according to the invention. FIG. 4 shows different iteration steps for a distance-based selection criterion in the input / output quantity range of the method according to the invention. FIG. 6 shows a comparison of various selection criteria using a conventional method for identifying models. FIG. 6 shows a comparison of various selection criteria using a conventional method for identifying models. FIG. 6 shows a comparison of various selection criteria using a conventional method for identifying models. It is a figure which shows the comparison of the mean square error at the time of using the conventional method which specifies a model, and the case where various selection criteria are used. It is a figure which shows about application of the method by this invention in calculating the model regarding NOx discharge | emission of an internal combustion engine. It is a figure which shows about application of the method by this invention in calculating the model regarding NOx discharge | emission of an internal combustion engine.

  For the method according to the invention, it is first necessary to select one model with a certain model structure. Using the model structure, the behavior of the technical system with respect to the characteristic value, ie the output quantity depending on the specific input quantity, must be estimated. The following description of the method will be described on the basis of a so-called local model network (LMN). However, the method can be similarly replaced with other known model structures, such as multilayer perceptrons, support vector machines, or Gaussian processes. Local model networks are superior in terms of lower computer costs, the availability of existing knowledge of technical systems and model parameters that can be used to design experiments in a robust manner and are therefore particularly suitable for the method according to the invention. ing. For this reason, the invention will be described below based on a local model network (LMN) as a model structure.

  The local model network (LMN) is composed of the following I local models.

(Hereinafter, in this specification, the ∧ symbol on the character may be written on the right shoulder of the character.)

They are only effective locally, ie only for certain input quantities. Here, u indicates an n-dimensional input quantity vector of a technical system including all input quantities, and θ _j is a model parameter of the jth local model. Here, the local model y ^ _j (u; θ _j ) is a quadratic multiple regression model having an interaction term. However, other model structures related to the local model, such as a linear or cubic multiple regression model, for example. Note that can also be used. The output y ^ (u) of the local model network is a weighted sum of the outputs of the local model y ^ _j (u; θ _j ) and is an estimated value related to the output of the system. For this purpose, the following efficacy function is defined.

(Hereinafter, in this specification, the symbol “˜” on the character may be written on the right shoulder of the character.)

This efficacy function defines the efficacy range (effective range) of the local model ＾ _j (u; θ _j ), where x ^~ means the selected input quantity of the input quantity vector u. Thus, as is well known, the output of the local model network y ^ (u) is

The local model network (LMN) requires training data (Training data) in order to estimate the relationship between the input quantity u and the technical system output quantity y. By training in the training unit 2, in addition to the model parameter θ _j , the number I of the local models y ^ _j (u; θ _j ) and the effectiveness function Φ _j (x ^˜ ) can be specified. This itself is sufficiently understood from Non-Patent Document 2, and will not be described in detail here. The training data is derived from an experimental design created as described below with reference to FIG.

The premise is that the model does not have to make an accurate estimation in all possible output ranges, but only in a certain target output range, for example, the internal combustion engine is calibrated and specified. particular output quantity with respect to the input amount (e.g., those such as nO _x emissions and soot emissions) of is that must to meet certain criteria. Therefore, although the target output amount range is known, the input amount of the model corresponding to it is not known. Therefore, these input quantities are identified, and the model parameter θ _j of the model is parameterized (determining the parameters) with respect to the target output quantity range (and possibly also the number of local models I and its efficacy function). The experimental design is necessary.

  The experimental design is a sequence of input quantities (and sometimes a temporal sequence), and these input quantities are set on a technical system test bench and the desired output quantity of the technical system is accompanied by it. Observed or measured. For example, a test system such as an engine test table is provided with a technical system such as an internal combustion engine, and in some cases, a load device such as an electric dynamometer is connected to the test table or a technical system or load device. Are operated according to the experimental design.

The experimental design is based on an iterative selection of an input quantity vector u _cand from a certain input quantity vector set U _cand . As the input quantity vector set U _cand , any _conceivable arbitrary set of input quantity vectors u _cand that covers the entire input quantity range as uniformly as possible can be used. The input quantity vector set U _cand is predetermined and is assumed to be known with respect to the method process.

One input quantity vector u _cand can be used only once in the experimental design. At the start of the method process, a set U _start of a plurality of input quantity vectors u _start is set. Thus, at each iteration step, a new input quantity vector u _new is first selected from the input quantity vector set U _{start and then} from the input quantity vector set U _cand and the technical relation for these input quantity vectors u _new The response of a simple system is measured in the form of an output y _new through a test bench experiment in the test bench 1 for a technical system. (Including the new input quantity vector _{u new new.)} Known as or selected input quantity vector _{u app} set _{U app} and set _{Y app} of the measured output quantities _{y app} in correspondence of the training unit 2 Training data (Trainingsdaten) for training the local model network (LMN) is formed in (e.g., a qualified electronic computer with software and an execution algorithm for performing training). Thus, at each iteration step k, the local model network (LMN) is trained with these training data. Training can also cause changes in the local model network (LMN), such as a change in network dimension I and a change in model parameter θ _j , only in a considerable number of iteration steps. When the model is changed, the model parameter θ _j and possibly the number I of local models y ^ _j (u; θ _j ) and its effectiveness function Φ _j (x ^˜ ) are determined by the local model network (LMN). Updated according to the rules. This is as described in Non-Patent Document 2, for example.

Thus, until a sufficiently accurate model LMN _fin for the target output range is obtained, the set U _{app of} the already selected input quantity vectors u _app continues to increase, and the set of measured output quantities y _app that are in a corresponding relationship Y _app keeps increasing. This can be determined by appropriate stop conditions such as, for example, the maximum number of training data and a threshold value (the mean square model error within the target output range must fall below this). Here, the selection of a _new input quantity vector u _new is performed by the following method process.

First, based on the current local model network (LMN) at each iteration step k, an output quantity y ^ (u _cand ) (y ^ _cand ) estimated from the current model is calculated for the input quantity vector set U _cand. .
Next, from this result, all the input quantity vectors u _{cand and COR} are specified, and the estimated output quantities y ^ _{cand and COR} of these input quantity vectors are defined as a target output quantity range (custom output range, COR) (this The range is defined by COR = [y _min ; y _max ] by its boundaries y _min and y _max .) These input quantity vectors are integrated into the target input quantity vector set U _{cand, COR} .

Now, from this target input quantity vector set U _{cand, COR} , a new input quantity vector u _new is selected every time at each iteration step k. At that time, a distribution as uniform as possible is obtained in the input quantity space, the output quantity space, or the input / output quantity space. The background is that the local model network LMN, ie the model in general, is more accurate in the vicinity of the training data than at a distance from the training data. If training data is distributed as uniformly as possible, the resulting model uncertainty is reduced. For these reasons, the selection of a _new input quantity vector u _new is also known as a distance-based criterion (S-optimals design or maximum / minimum distance design). Is applied). In this case, the goal of the selection criterion based on distance is to maximize the minimum distance between the design points (here, input and / or output). In this regard, selection criteria based on the following three distances can be defined.

Selection criteria based on distance in the input volume range:
From the target input quantity vector set U _{cand, COR} , each input quantity vector u _{cand, COR} is selected as a _new input quantity vector u _new , which is the minimum for a known input quantity vector u _app in the set U _app . The Euclidean distance becomes as large as possible, and the following equation is established.

  This criterion results in a uniform distribution of the selected input quantity vector in the input quantity range.

Selection criteria based on distance in output volume range:
First, the output quantity y ^ (u _{cand, COR} ) is calculated for the input quantity vector set U _{cand, COR} using the current effective model. The new input quantity vector u _new has the following output quantities:

That is, this output amount is such that the minimum Euclidean distance with respect to the known output amount is as large as possible, and a new input amount vector u _new having a correspondence relationship is given by the following expression.

  This criterion provides a uniform distribution of the output amount in the target output amount range.

Selection criteria based on distance in input range / output range:
Here, the already selected input quantity vector U _app is supplemented by the output quantity Y _app having a corresponding relationship,

Thus, the target input quantity vector set U _{cand, COR} is supplemented by the estimated output quantity y ^ (U _{cand, COR} ) that is in a correspondence relationship,

It becomes. A new input quantity vector u _new is given by this criterion as follows.

  Here, an input quantity having the smallest Euclidean distance with respect to the known input quantity and the corresponding output quantity having the largest possible Euclidean distance with respect to the known output quantity is obtained. This criterion results in a uniform distribution of input quantities in the input quantity range and a uniform distribution of output quantities in the target output quantity range.

The local model network LMN _fin trained in this way is thus able to estimate the output y of the technical system with the desired accuracy (set by the selected stop condition) within the target output range. it can. A trained model network (LMN) is thus used, for example, for the development of technical systems, for example to calibrate the control unit of an internal combustion engine in such a way that the defined limits for output power are observed. Can do.

According to FIGS. 2 to 4, a selection criterion based on a bath tub-like function f (y = f (u)) that depends on a one-dimensional input amount u, and further based on a distance in the input amount range / output amount range. Based on this, the method according to the present invention will be described specifically. This function f shows strong non-linear behavior within the input quantity ranges u = [0; 0.2] and u = [0.8; 1], and the input quantity range u = [0.2; 0.8. ] Is almost straight. The target output quantity range in which the model (local model network LMN) must be parameterized sufficiently accurately shall be defined by, for example, y _min = 0.15 and y _max = 1. Curve 3 in FIG. 2 shows a starting model with three selected starting input quantities u _start in the set U _app . Two broken lines are marks of the target output amount range. For each axis, the frequency of points in the input and output ranges is shown in the form of bars. The newly calculated input quantity u- _new based on the method process is shown in the same way in FIG. FIG. 3 shows a model based on the selection of seven input quantities in the set U _app and the response of the current model in the form of an output quantity y _app . FIG. 4 shows a model with selection of 11 input quantities in the set U _app, in which the process is terminated (no more new input quantities u- _new are taken into account). 2 to 4, the method process systematically parameterizes the model (determines the model parameters) within the determined target output range, and as a result, the model is very accurate within the target output range. On the other hand, it turns out to be inaccurate outside this range. It can also be seen from the frequency distribution that for the important target output range, the point distribution is very uniform in the input range and output range (depending on the selected selection criteria). In addition, it can be seen that the two arcs of the output function can be covered uniformly.

  5-7 compare various selection criteria based on distance with 11 selected input quantities each. FIG. 5 shows the result of the method according to the prior art that does not use the target output amount range. Although the input quantities are certainly evenly distributed, it can be seen that the model is not useful in the target output quantity range because none of the input quantities were parameterized with output quantities within the target output range. In FIG. 6, a selection criterion based on the above-described distance in the input amount range is applied, and as a result, four input amounts having an output amount within the target output amount range are selected. In FIG. 7, a selection criterion based on the above-described distance in the output amount range is applied, and as a result, six input amounts having an output amount within the target output amount range are selected.

FIG. 8 further shows the mean square error (MSE) of the different methods (according to a logarithmic scale). In the figure, curve 4 shows MSE according to a method not using the target output amount range, curve 5 shows a method using a selection criterion based on the distance in the input amount range, and curve 6 shows a distance in the output amount range. And a curve 7 shows a method using a selection criterion based on the distance in the input quantity range / output quantity range. Clearly, a distance-based selection criterion that simultaneously considers the target output range will improve the quality of the model compared to the method without the target output range in that it significantly improves the modeling error. . Here, qualitatively, the selection criterion based on the distance in the input amount range / output amount range seems to be superior to the selection criterion based on other distances.
Model-based design of experiments using target output ranges is an efficient method, which allows a technical process model to be parameterized in the target output range, thereby reducing the input range. This leads to further improvement of the model quality within the target output amount range. At the same time, this reduces the number of required test bench experiments required to obtain the same model quality.

Hereinafter, at a specific rotation speed and a specific load, the input amount depends on the throttle valve state (S), fuel pressure (p), and exhaust gas recirculation (Abgasrueckfuehrung (EGR)) (input amount vector u). The method according to the present invention will be described by taking a practical example of the form of NOx emission of the internal combustion engine (output y). As the target output amount range, NO _x emission is set to y _min = 0.1 × 10 ⁻⁵ Kg / s and y _max = 0.4 × 10 ⁻⁵ kg / s. The underlying model (here, for example in the form of a local model network (LMN)) is systematically parameterized with respect to the target output range based on the method according to the invention. As can be seen in FIG. 9, with this model the output quantity is estimated in the target output quantity range by the method according to the invention. In the figure, curve 8 shows the results for the 11 selected input quantities for a method that does not use the target output quantity range, and curve 9 shows the results using the selection criteria based on the distance in the input quantity range. A curve 10 shows a result using a selection criterion based on the distance in the output amount range, and a curve 11 shows a result using a selection criterion based on the distance in the input amount range / output amount range. Finally, FIG. 10 shows the NO _x emissions estimated by the calculated model for a constant throttle valve state S = 0.1 and for a specific speed and a specific load.

Claims (5)

A method for calculating a model for an output quantity (y) of a technical system that depends nonlinearly on a plurality of input quantities in the form of an input quantity vector (u), wherein the model has a plurality of model parameters as a model. A model structure is set, the model parameters are optimized iteratively based on measured output quantities from a plurality of test bench experiments in the technical system, and a plurality of the test bench experiments are performed according to an experiment plan, The experimental design is respectively created from the estimated output quantity (y ^) of the model for each iteration step (k),
The following method steps,
Using the model effective for the current iteration step (k), from a set (U _cand ) of a plurality of input quantity vectors (u _cand ) to a set of estimated output quantities (y ^ (u _cand )) ( y ^ (U _cand )) is calculated,
Resulting in the output of the set _{(y ^ (U cand))} from the estimated output of target output quantity range (COR) which is set in advance _{(y ^ (u cand))} , the target input quantity vector set _{(U cand , COR} ) a target input quantity vector (u _{cand, COR} ) is specified,
The target input quantity vector set _{(U cand, COR)} from, for the next iteration step (k + 1), a set of new input quantity vector _{(u new new)} is already selected input amount vector _{(u app)} ( U _app ), at which time the new input quantity vector (u _new ) is selected based on a predetermined distance-based selection criterion;
The set (U _app ) based on the selected input quantity vector (u _app ) expanded in this way is used as an experiment plan, so that measurement data of the output quantity (y _app ) is generated based on the test bench experiment. Wherein the model is optimized using the measured data , and the method steps are repeated iteratively until a set stop condition is met. 2. A method according to claim 1, wherein the input quantity vector has a minimum Euclidean distance as large as possible with respect to the known input quantity vector (u _app ) in the set (U _app ) of the input quantity vectors already selected. (U _{cand, COR} ) is selected from the target input quantity vector set (U _{cand, COR} ) as a _new input quantity vector (u _new ). The method according to claim 1, wherein an output quantity (y ^ (u _{cand, COR} )) is calculated for the target input quantity vector set (U _{cand, COR} ) using the currently effective model, and a new When the input quantity vector (u _{cand, COR} ) is selected as the input quantity vector (u _new ), the output quantity (y ^ (u _{cand, COR} ) estimated for the input quantity vector (u _{cand, COR} ) )) Is selected such that the input quantity vector (u _{cand, COR} ) has the smallest possible Euclidean distance with respect to the known output quantity (y _app ). The method according to claim 1, wherein the set of already selected the input quantity vector _{(U app),} along with supplemented by the output quantity in correspondence _{(Y app),} the target input quantity vector set _{(U cand , COR} ) is supplemented by the estimated output amount (y ^ (U _{cand, COR} )) in the corresponding relationship, and the input amount vector (u _{cand, COR} ) is selected as the _new input amount vector (u _new ). In addition, the input quantity vector (u _{cand, COR} ) has a minimum Euclidean distance as large as possible with respect to the known input quantity vector (u _app ), and has a corresponding relationship with the input quantity vector (u _{cand, COR} ). A _{minimum Eucli whose} output quantity (y ^ (u _{cand, COR} )) is as large as possible with respect to the known output quantity (y _app ). The input quantity vector (u _{cand, COR} ) is selected to have a _grid distance. 2. The method according to claim 1, comprising a predetermined number (I) of a local model (y ^ _j (u; θ _j )) having a model parameter (θ _j ) and a corresponding efficacy function (Φ _j (x ^˜ )). A local model network (LMN) is used as a model, and in one iteration step (k), based on the selected input quantity vector (u _app ) and the measured output quantity (y _app ), the local model network (LMN) is used. That the number (I) of the model (y ^ _j (u; θ _j )), the model parameter (θ _j ), and / or the corresponding efficacy function (Φ _j (x ^˜ )) is adjusted. Feature method.

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